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Outline: The goal of this course is to give students a zoomed-out perspective on algebraic geometry. This course starts with the introduction of affine varieties, schemes and sheaves, before introducing projective varieties, morphisms and fibre products. We will motivate the main definitions, discuss the basic results and provide plenty of examples.
The course ends with the introduction of vector bundles, (quasi-)coherent sheaves and sheaf cohomology, again with lots of examples from different areas.